Optical spectrum augmentation for machine learning powered spectroscopic ellipsometry

Area of Science:

• Semiconductor Manufacturing
• Metrology
• Data Science

Background:

• Complex semiconductor structures necessitate accurate measurement systems for mass production.
• Repeatability and reproducibility are critical alongside accuracy when using multiple measuring instruments.
• Existing methods for improving measurement accuracy often overlook inter-instrument variability.

Purpose of the Study:

• To develop a data augmentation approach to minimize physical differences between multiple measuring instruments in spectroscopic ellipsometry (SE).
• To propose stochastic polynomial wavelength calibration (s-PWC) for enhancing Gage repeatability and reproducibility (Gage R&R) values.
• To evaluate the effectiveness of s-PWC in improving nanostructure prediction models for 3D vertical NAND Flash memories.

Main Methods:

• Modeling photodetector misalignment as polynomials and incorporating random noise.
• Applying a data augmentation approach using domain knowledge in spectroscopic ellipsometry.
• Training nanostructure prediction models with industrial datasets before and after applying s-PWC.

Main Results:

• The proposed s-PWC method reduced the average Gage R&R percentage from 10.23% to 6.3%.
• Comparative methods, Gaussian noise augmentation (GNA) and polynomial wavelength calibration (PWC), resulted in Gage R&R values of 10.01% and 7.62%, respectively.
• Coefficient of determination (R²) and root mean square error (RMSE) remained largely unchanged, indicating maintained predictive accuracy.

Conclusions:

• s-PWC ensures consistent predictions from inferential models across multiple measuring instruments without compromising accuracy.
• The methodology provides a guideline for enhancing machine learning and SE model performance in mass production.
• Future work could explore data augmentation for other physical component differences to further improve R² and RMSE.